A furnace burns a liquid coal tar fuel derived from coke-ovens. Calculate the heat transferred in the furnace if the combustion gases leave at 1500 K. The burners operate with 20 per cent excess air. Take the fuel supply temperature as 50ºC (323 K) and the air temperature as 15ºC (288 K).

Question

The properties of the fuel are:

Carbon 87.5 per cent w/w

Hydrogen 8.0

Oxygen 3.5

Nitrogen 1.0

Sulphur trace

Ash balance

Net caloriﬁc value 39,540 kJ/kg

Latent heat of vaporisation 350 kJ/kg

Heat capacity 1.6 kJ/kg K

[latex]\ C^{º}_{p} [/latex] of gases, kJ/kmol K

[latex]\ C_{p} =A+BT+CT^{2} +DT^{3} [/latex]

D	C	B	A	Camponent
1 [latex]\ CO_{2} [/latex]	-5.518E-5	7.332E-2	19.763	1 [latex]\ CO_{2} [/latex]
2 [latex]\ H_{2}O [/latex]	10.538E-6	19.207E-4	32.190	2 [latex]\ H_{2}O [/latex]
3 [latex]\ O_{2} [/latex]	17.431E-6	-3.674E-6	28.06	3 [latex]\ O_{2} [/latex]
4 [latex]\ N_{2} [/latex]	26.752E-2	-1.354E-2	31.099	4 [latex]\ N_{2} [/latex]

Accepted Answer

Material balance

Basis: 100 kg (as analysis is by weight).

Assume complete combustion: maximum heat release.

Reactions: [latex]\ C+O_{2} ightarrow CO_{2} [/latex]

[latex]\ H_{2} +\frac{1}{2}O_{2} ightarrow CO_{2} [/latex]

Element	kg	kmol	Stoichiometric kmol	kmol, products
C	87.5	7.29	7.29	7.29,[latex]\CO_{2} [/latex]
[latex]\ H_{2} [/latex]	8.0	4.0	2.0	4.0,[latex]\ H_{2}O [/latex]
[latex]\ O_{2} [/latex]	3.5	0.11	-	0.11
[latex]\ N_{2} [/latex]	1.0	0.04	-	0.04
Total		11.44	9.29

[latex]\ O_{2} [/latex] required with 20 per cent excess = 9.29×1.2=11.15 kmol.

Unreacted [latex]\ O_{2} [/latex] from combustion air = 11.15-9.29=1.86 kmol.

[latex]\ N_{2} [/latex] with combustion air = [latex]\ 11.15 imes \frac{79}{21}=41.94 [/latex]
Composition of combustion gases:

[latex]\ CO_{2} =7.29kmol [/latex]

[latex]\ H_{2}O=4.0 [/latex]

[latex]\ O_{2} 0.11+1.86=1.97 [/latex]

[latex]\ N_{2} 0.04+41.98 [/latex]

Presentation of data to the program:

[latex]\ C_{p} [/latex] of fuel (component 5), taken as constant,

A=1.6, B = C= D = 0

Heat of reaction and latent heat, taken to be values at datum temperature of 298 K. There is no need to convert to kJ/kmol, providing quantities are expressed in kg. For the purposes of this example the dissociation of [latex]CO_{2} [/latex] and [latex]H_{2}O [/latex] at 1500 K is ignored.

Question 3.14: A furnace burns a liquid coal tar fuel derived from coke-ove...

Related Answered Questions